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Prediction in a non-homogeneous Poisson cluster model

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  • Matsui, Muneya

Abstract

A non-homogeneous Poisson cluster model is studied, motivated by insurance applications. The Poisson center process which expresses arrival times of claims, triggers off cluster member processes which correspond to number or amount of payments. The cluster member process is an additive process. Given the past observations of the process we consider expected values of future increments and their mean squared errors, aiming at application in claims reserving problems. Our proposed process can cope with non-homogeneous observations such as the seasonality of claims arrival or the reducing property of payment processes, which are unavailable in the former models where both center and member processes are time homogeneous. Hence results presented in this paper are significant extensions toward applications.

Suggested Citation

  • Matsui, Muneya, 2014. "Prediction in a non-homogeneous Poisson cluster model," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 10-17.
    • Handle: RePEc:eee:insuma:v:55:y:2014:i:c:p:10-17
    DOI: 10.1016/j.insmatheco.2013.12.001
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    References listed on IDEAS

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    1. Norberg, Ragnar, 1993. "Prediction of Outstanding Liabilities in Non-Life Insurance1," ASTIN Bulletin, Cambridge University Press, vol. 23(1), pages 95-115, May.
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    Cited by:

    1. Avanzi, Benjamin & Taylor, Greg & Wong, Bernard & Yang, Xinda, 2021. "On the modelling of multivariate counts with Cox processes and dependent shot noise intensities," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 9-24.
    2. Muneya Matsui, 2017. "Prediction of Components in Random Sums," Methodology and Computing in Applied Probability, Springer, vol. 19(2), pages 573-587, June.
    3. Benjamin Avanzi & Gregory Clive Taylor & Bernard Wong & Xinda Yang, 2020. "On the modelling of multivariate counts with Cox processes and dependent shot noise intensities," Papers 2004.11169, arXiv.org, revised Dec 2020.

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